Papert's Microworld and Geogebra: a Proposal to Improve Teaching Of

Creative Education, 2019, 10, 1525-1538 http://www.scirp.org/journal/ce ISSN Online: 2151-4771 ISSN Print: 2151-4755 Papert’s Microworld and Geogebra: A Proposal to Improve Teaching of Functions Carlos Vitor De Alencar Carvalho1,4, Lícia Giesta Ferreira De Medeiros2, Antonio Paulo Muccillo De Medeiros3, Ricardo Marinho Santos4 1State University Center of Western, Rio de Janeiro, RJ, Brazil 2CEFET/RJ, Valença, RJ, Brazil 3Rio de Janeiro Federal Institute (IFRJ), Pinheiral, RJ, Brazil 4Vassouras University, Vassouras, RJ, Brazil How to cite this paper: De Alencar Car- Abstract valho, C. V., De Medeiros, L. G. F., De Me- deiros, A. P. M., & Santos, R. M. (2019). This paper discusses how to improve teaching of Mathematics in Brazilian Papert’s Microworld and Geogebra: A Pro- schools, based on Seymour Papert’s Constructionism associated with Infor- posal to Improve Teaching of Functions. mation Technology tools. Specifically, this work introduces the construction- Creative Education, 10, 1525-1538. https://doi.org/10.4236/ce.2019.107111 ist microworld, a digital environment where students are able to build their knowledge interactively, in this case, using dynamic mathematics software Received: June 6, 2019 GeoGebra. Accepted: July 14, 2019 Published: July 17, 2019 Keywords Copyright © 2019 by author(s) and Microworld, GeoGebra, Seymour Papert, Information Technologies in Scientific Research Publishing Inc. Education This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access 1. Introduction This research’s main goal is to present a proposal to help Brazilian teachers improve their educational practices. Many of them are not familiar with Informa- tion Technologies (IT) and do not know how to use educational softwares in their classrooms. Abellón (2015) informs that only 2% of Brazilian teachers use TI in their classes, mainly due to lack of access to computers, lack of formal training in pedagogical softwares and low-speed Internet connection. He further details that there is, on average, one computer for every 34 students in Brazil’s schools. Consequentially, several Brazilian teachers still follow traditional pedagogical techniques, where they require students to memorize contents in a rigid, me- chanic way. Freire (1987) describes this process as “bank style education”, where DOI: 10.4236/ce.2019.107111 Jul. 17, 2019 1525 Creative Education C. V. De Alencar Carvalho et al. teachers “deposit” information in students “empty” minds. However, this conception is not adequate for modern students, since they use IT massively even before they enter school. They are skilled in using social media and expect to have instant access to information through Internet. Their minds are far from “empty” and traditional educational methods used by many teachers end up frustrating them. D’Ambrosio (1991) defines these methods as “obsolete, uninteresting and useless”. As a result, this study intends to present a proposal to improve teaching of Mathematics using Seymour Papert’s Constructionism associated with Informa- tion Technology (IT) tools. It aims to describe how to use a dynamic mathematics software, like GeoGebra, to build an interactive environment suitable to modern students.to create these components, incorporating the applicable crite- ria that follow. 2. Papert’s Constructionism School has not changed much for a long time. New technologies and media have little influence on how teaching and learning happen in classrooms. Ripper (1996) affirms that many educational systems still prepare its students to execute repetitive tasks without questioning, a style of work that dates back to XIX century. However, modern jobs demand creative and proactive workers, able to adapt to new challenges and circumstances. In consequence, schools have to de- part its traditional posture and change to face those demands. Papert (1992) describes this situation using a parable, where he imagines teachers traveling through time from a century ago to visit a contemporary classroom. While some objects might look strange, the teachers would easily recognize the place as a classroom, very similar to the ones in their own time. This parable leads to a question: “Why, through a period when so much human activity has been revolutionized, have we not seen a comparable change in the way we help our children learn?” (Papert, 1992: p. 2) These traditional methods lead to dissatisfaction among modern students. “To the extent that children reject School as out of touch with contemporary life, they become active agents in creating pressure for a change. Like any other social structure, School needs to be accepted by its participants. It will not sur- vive very long beyond the time if children can no longer be persuaded to accord it a degree of legitimation” (Papert, 1992: p. 6). Born in South Africa, Papert initially did research in Mathematics at Cam- bridge University, and later worked with Jean Piaget at University of Genève. This experience in Switzerland motivated him to study how children build their knowledge (Papert, 1992), for Piaget’s theory provided a comprehensive frame- work to understand how youngsters think of different phases of their lives. “Piaget’s constructivism offers a window into what children are interested in, and able to achieve, at different stages of their development. The theory describes how children’s ways of doing and thinking evolve over time, and under which circumstance children are more likely to let go of—or hold onto—their DOI: 10.4236/ce.2019.107111 1526 Creative Education C. V. De Alencar Carvalho et al. currently held views” (Ackerman, n.d.). Starting from that perspective, Papert developed his own theory, Constructiv- ism, which focus “on the art of learning, or ‘learning to learn’”, and on the signi- ficance of making things in learning” (Ackerman, n.d.). He emphasizes the im- portance of interacting with educational artifacts to facilitate the construction of new knowledge. “The word constructionism is a mnemonic for two aspects of the theory of science education underlying this project. From constructivist theories of psy- chology, we take a view of learning as a reconstruction rather than as a transmis- sion of knowledge. Then we extend the idea of manipulative materials to the idea that learning is most effective when part of an activity the learner experiences as constructing a meaningful product” (Sabelli, 2008). Later, Papert worked in Massachusetts Institute of Technology (MIT), where he developed LOGO programming language, specially designed as a construc- tionistic educational environment, quite effective for teaching Mathematics. Pa- pert even created the term mathfobia, to describe the fear and discomfort most students have towards Mathematics (Fainguelernt, 1999). Constructionism defends computers as a tool for knowledge building, interacting with students in a cycle known as D-E-R-D (description-execution- reflection-debug). Description involves a thorough analysis of the problem, allowing students to understand what has to be accomplished. In the execution phase, students interact with the software and receive instantaneous feedback, which leads to the reflection phase, where results are analyzed. Finally, the debug phase discusses new strategies and views (Valente, 1999), as shown in Figure 1. Papert considers the tendency to overvalue abstract reasoning an obstacle in Education progress. He believes in an “epistemological reversion to more concrete ways of knowing—a reversal of the traditional idea that intellectual progress consists of moving from the concrete to the abstract” (Papert, 1992: p. 137). His theory preconizes to produce the most learning with the least teaching, allowing students to freely discover new knowledge by themselves. In fact, Figure 1. Cycle “description-execution-reflection-debug” (Valente, 1999). DOI: 10.4236/ce.2019.107111 1527 Creative Education C. V. De Alencar Carvalho et al. “the kind of knowledge children most need is the knowledge that will help them to get more knowledge” (Papert, 1992: p. 139). A practical example would be how children learn to play videogames. They assimilate complex rules and strategies without formal training by a teacher, and use their own initiative to look for information in any type of media. In short, they build new knowledge in their personal way and use what they already know as a starting point. Papert describes these innate skills as learning without teaching, and these ab- ilities help students to lose their fear towards learning Mathematics, previously described as mathfobia. Fainguelernt (1999) states that LOGO programming language is an efficient learning tool for Math students, for its constructionist approach allows them to build their knowledge interacting with the computer at their own pace and time. However, traditional ways are hard to change, and most schools did not understand how to insert computers and constructionist softwares in their educational routine. “The computer in the classroom was undermining the division of knowledge into subjects; it was turned into a subject of its own. It undermines the idea of curriculum; it was made the topic of a curriculum of its own. Nevertheless, of course, this mechanism is not confined to computers. In its time, School has normalized other subversive influences too. For example, Piaget was the theorist of learning without curriculum; School spawned the project of developing a Pia- getian curriculum” (Papert, 1992: p. 54). As a result, Courses aiming to achieve computer literacy were developed (Va- lente, 1995). School started teaching how to use computers as an end in itself, as another discipline in its curriculum, and not as a pedagogic tool to help improve learning of every other discipline. In sequence, computers were transformed into instructional tools. In other words, they received the exact material used in traditional classes only to trans- mit it to students, who are passive subjects in the whole process. Computers work as optimized teaching machines, and teachers have little influence on the learning experience (Valente, 1995).

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